The World is a Theatre

TA. The World is a Theatre

There are n boys and m girls attending a theatre club. To set a play “The Big Bang Theory”, they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.

Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.

Input

The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).

Output

Find the required number of ways.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

Example

Input

5 2 5

Output

10

code

#include<bits/stdc++.h>
#define int long long
#define endl '\n'
 
using namespace std;


const int N = 40,INF=0x3f3f3f3f,mod=1e9+7;
 
typedef pair<int,int> PII;

int T=1;
int c[N][N];

void init() //递推预处理出所有组合
{
    for(int i=0;i<N;i++)
        for(int j=0;j<=i;j++)
            if(!j) c[i][j]=1;
            else c[i][j]=(c[i-1][j-1]+c[i-1][j]) % mod;
}

void solve(){
	init();
	int n,m,t;
	cin>>n>>m>>t;
	int ans=0;
	for(int i=4;i<=n && t-i>0;i++){
		if(t-i<=m){
			ans+=c[n][i]*c[m][t-i];
		}
	}
	cout<<ans<<endl;
}

signed main(){
//	cin>>T; 
    while(T--){
        solve();
    }
    return 0;
}